Non-equilibrium dynamics in chemical systems. Proceedings of the International Symposium, Bordeaux, France, September 3-7, 1984
The study of chemical systems under conditions removed from the thermodynamic equilibrium when the kinetic laws are nonlinear constitutes today one of the most fascinating research fields for chemist-physicists, physicists and also for mathematicians. Until about twenty years ago we regarded chemical reactions as the result of the collisions among the molecules in their disorderly movement. This is true but only when the reactions occur in the neighbourhood of the thermodynamic equilibrium. In conditions removed from the thermodynamic equilibrium when obtaining the Bolousov-Zhabotinskij (B.Z.) reaction, which behaves like a chemical clock, we are obliged to think that among the intermediate molecular species a perfect coherence is achieved. Beginning in 1978 and up to the present a great number of chemical reactions have been obtained, in which the concentration of the intermediate species has periodic oscillations of a limit-cycle type. This book consists of seven parts structured on different aspects of the behaviour of the chemical systems maintained far from the thermodynamic equilibrium. The first part comprises the plenary conference ''Spatial and temporal configurations in systems far from the equilibrium''. The main idea which pervades the conference is that the appearance of the spatial and temporal structures is a general phenomenon. These structures appear in chemical optics (laser), hydrodynamic systems, in electronic, solid, acoustic devices and others on the condition that the systems are maintained far from the thermodynamic equilibrium. The second part, entitled ''Oscillatory reactions and modeling problems'', as the title indicates, contains papers which deal with the periodic oscillations of the intermediate species concentration. The papers present both the experimental and the theoretical results of the chemical oscillations. As the works in the second part only take into account the periodic oscillations of the concentrations, those in the third part, entitled ''Spatial structures and chemical waves'', also consider the diffusion responsible for the presence of spatial structures and of chemical waves which travel in the whole volume of the reactant system. If a chemical system, which has periodic oscillations of a limit-cycle type, is submitted to a more drastic compulsion at the limit (the thermodynamic forces are increased) then the system deviates even more from the thermodynamic equilibrium condition. In this case the system makes the transition from periodic oscillations of a limit-cycle type to a state of chaos. This condition is characterized by nonperiodic oscillations. The chaos condition in chemical systems is analyzed in the fourth part entitled ''Chemical chaos''. In the fifth part, ''Noise effects'', there are papers which study external noise influence on the structural stability of the systems with self- organization. Where the chemical, hydrodynamic, optical and other systems are maintained far from the thermodynamic equilibrium, the interval fluctuations which appear can be amplified and can change completely the previous behaviour of the system. Out of a disorganized system, an ordered system can be born. This is the case of Bénard instability from hydrodynamics. The importance of the fluctuations in the appearance of the ordered systems is studied in the sixth part, ''Stochastic analysis''. In the seventh part, and the last one, the summaries of the works of Poster are presented. After reading through the entire book, a general remark is appropriate and that is: Structural and functional order is not only specific to biological systems but this can appear in systems kept far from the thermodynamic equilibrium where the processes are completely nonlinear. The birth of life is the natural result of the evolution of the systems which lack life with self-organization towards more and more complex structures.
periodic oscillations of a limit-cycle type
scientific article; zbMATH DE number 3905489